Explaining the Applicability of Mathematics in Science

Philosophical discussion of applied mathematics has tended to focus on a cluster of related 'problems of applicability' that are often conflated. In this paper, I argue that several of these problems raise no significant philosophical issues. I then identify two particular aspects of the involvement of mathematics in science: that mathematics is indispensable for science, and that mathematics sometimes plays an explanatory role in science. I argue that there are genuine questions surrounding these two features of applied mathematics, and in particular that the issue of the role of mathematics in scientific explanation has ramifications for the debate between realist and anti-realist views in the philosophy of mathematics.